# What is the vertex form of #y= 8x^2+17x+1 #?

##### 1 Answer

Jan 26, 2016

# y =8 (x + 17/16 )^2 - 257/32 #

#### Explanation:

The vertex form of the trinomial is;

#y = a(x - h )^2 + k# where (h , k ) are the coordinates of the vertex.

the x-coordinate of the vertex is x

# = -b/(2a)# [from

# 8x^2 + 17x + 1 # a = 8 , b = 17 and c = 1 ]

so x-coord

# = -17/16 # and y-coord

# = 8 xx (-17/16)^2 + 17 xx (-17/16) + 1 #

# = cancel(8) xx 289/cancel(256) - 289/16 + 1#

# = 289/32 - 578/32 + 32/32 = -257/32# Require a point to find a: if x = 0 then y=1 ie (0,1)

and so : 1= a

#(17/16)^2 -257/32 = (289a)/256 -257/32# hence

# a = (256 + 2056)/289 = 8# equation is :

# y = 8( x + 17/16)^2 - 257/32#